Question

Identify whether the following expression is a polynomial. If it is, identify the type according to the number of terms.

Answer 1

Answer:

The expression is a polynomial.

Trinomial (according to the number of terms)

Step-by-step explanation:

Given the algebraic expression, 6x² + x + 1:

A term comprises of a product of numerical coefficient and one of more variables raised to powers.  Like terms have the same variables and exponents.

While a polynomial is a term (or finite sum of terms), comprising of variables with positive or zero integer exponents. Strictly defined, the terms within a polynomial expression cannot include variables as a denominator.  

A monomial is a single-termed polynomial.

A binomial is a polynomial with two terms.

A trinomial is a polynomial that has exactly three terms.

With these given definitions, we can infer that the given polynomial expression, 6x² + x + 1,  is a trinomial, given that it has three terms:

• 6x² is the leading term with the highest degree or exponent. Specifically, the name of this term is quadratic, given its exponent of 2.
• x is a linear term, given its exponent of 1.
• 1 is a constant term.

Therefore, the given expression is a polynomial containing three terms, making it a trinomial.